Lagrangian and Geometric Analysis of Finite-time Euler Singularities

We present a numerical method of analyzing possibly singular incompressible 3D Euler flows using massively parallel high- resolution adaptively refined numerical simulations up to 81923 mesh points. Geometrical properties of Lagrangian vortex line segments are used in combination with analytical non-blowup criteria by Deng et al. [Commun. PDE 31 (2006)] to reliably distin- guish between singular and near-singular flow evolution. We then apply the presented technique to a class of high-symmetry initial conditions and present numerical evidence against the formation of a finite-time singularity in this case.